Consider the following hypothesis test: H0: p 0.75 Ha: p < 0.75 A sample of 400

Question

Consider the following hypothesis test:

H0: p 0.75
Ha: p < 0.75

A sample of 400 items was selected. Compute the p-value and state your conclusion for each of the following sample results. Use = .05.

Round your answers to four decimal places.

a. p = 0.62

p-value  

Conclusion:
p-value Selectgreater than or equal to 0.05, rejectgreater than 0.05, do not rejectless than or equal to 0.05, rejectless than 0.05, rejectequal to 0.05, do not rejectnot equal to 0.05, do not rejectItem 2  H0

b. p = 0.73

p-value  

Conclusion:
p-value Selectgreater than or equal to 0.05, rejectgreater than 0.05, do not rejectless than or equal to 0.05, rejectless than 0.05, rejectequal to 0.05, do not rejectnot equal to 0.05, do not rejectItem 4  H0

c. p = 0.7

p-value  

Conclusion:
p-value Selectgreater than or equal to 0.05, rejectgreater than 0.05, do not rejectless than or equal to 0.05, rejectless than 0.05, rejectequal to 0.05, do not rejectnot equal to 0.05, do not rejectItem 6  H0

d. p = 0.77

p-value  

Conclusion:
p-value Selectgreater than or equal to 0.05, rejectgreater than 0.05, do not rejectless than or equal to 0.05, rejectless than 0.05, rejectequal to 0.05, do not rejectnot equal to 0.05, do not rejectItem 8  H0

Explanation / Answer

Ans:

sample size,n=400

sampling distribution of sample proportions:

mean=p=0.75

standard error=sqrt(0.75*0.25/400=0.0217

left tailed test

a)

z=(0.62-0.75)/0.0217=-5.99

P(z<-5.99)=0

As,p-value<0.05,Reject H0

b)

z=(0.73-0.75)/0.0217=-0.92

p-value=P(z<-0.92)=0.1784

As,p-value>0.05,we Do not Reject H0.

c)

z=(0.7-0.75)/0.0217=-2.3

P(z<-2.3)=0.0107

As,p-value<0.05,we Reject H0.

d)

z=(0.77-0.75)/0.0217=0.92

p-value=P(z<0.92)=0.8216

As,p-value>0.05,we Do not reject H0.

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